Not just Islamic conquest but Arab conquest. Up to this point Arabs lived mainly in, well, Arabia. The indigenous peoples of Egypt, Syria, Iraq, etc..., were all non-Arab. Nowadays those indigenous groups are known as Copts, Syriacs, Chaldeans, etc...
Local populations adopted Arabic. Somewhat like, several centuries earlier, they adopted Greek; and elsewhere and at other times, Latin. The peoples of the regions were not replaced by Greek or Roman colonists.
And indigenous groups in France (just to use an example) are called Occitans, Bretons, Catalonians, Flemish, Alsatians, Corsicans, etc., etc. This isn't a unique phenomenon.
Flemish, Alsatians and Corsicans are literally Dutch, German and Italian, who are just part of France due to recent history. Occitans and Catalans are near Spain.
Bretons are Celts just like Gauls, whom you missed. You also missed other Celtic groups. And they (Celts) were the majority before invasions, still the majority.
Indigenous doesn't mean minority, it means the original inhabitants.
Legitimate question, in the early days was this a large distinction? Specifically, my understanding was that the earliest raids where this distinction is most accurate, they didn't actually change the local societies much. Mostly were raids for resources and did not stay.
That is, until the Islamic raids started, the indigenous groups took losses, but were not nearly as transformed. Is that not accurate?
Well, the distinction mattered. But because the distinction mattered, the modern labels aren't really accurate.
Arabs were the highest-prestige ethnicity within their empire. But they were numerically insignificant. You have "Arabs" and "Copts" in Egypt today, but most of the "Arabs" are Copts whose ancestors decided they wanted more respect. Same thing is true farther west, where the "Arabs" are Berbers.
That isn't really addressing my question, I don't think? The assertion is that most of the Arab mixing into region came at the same time as the later invasions. Yes, they would have remained fewer in absolute numbers. But they weren't even there after the earlier raids.